传递函数阵递阶随机梯度辨识方法的收敛性分析

阐述了递阶辨识原理，提出了传递函数阵模型参数的递阶随机梯度（HSG）辨识方法，在递阶辨识中，系统参数被分解为参数向量和参数矩阵，前者是由系统的特征多项式的系数构成的，后者是由传递函数矩阵分子多项式的系数构成的，借助于鞅超收敛定理的收敛性分析表明，HSG算法的参数估计误差一致有界；当持续激励条件成立时，参数估计误差一致收敛于零，递阶辨识方法具有计算量小和容易实现等特点。

Convergence of Hierarchical Stochastic Gradient Identification for Transfer Function Matrix Model

The hierarchical identification principle is stated, and the hierarchical stochastic gradient (HSG) algorithm for the transfer function matrix (TFM) model for multivariable systems is presented. In the hierarchical identification, the system parameters are divided into the parameter vector, which includes the coefficients of the characteristic polynomial of the system, and the parameter matrix, which includes the coefficients of the numerators of the TFM polynomials, respectively. The convergence analysis, using martingale hyperconvergence theorem, shows that the parameter estimation error (PEE) given by the HSG algorithm is consistently bounded, and that PEE consistently converges to zero under the persistent excitation condition. Hierarchical identification has a small amount of calculation and is easy to be realized.